From Krawtchouk to Hahn via Jacobi and some other applications of differential operators with polynomial coefficients

In the talk, we survey various known systems of polynomial eigenfunctions of linear differential operators with polynomial coefficients and show how the tridiagonalisation of differential operators introduced by E. Koelink and M. Ismail leads to simple relations between the Krawtchouk and Hahn polynomials. We discuss some other applications of the tridiagonalisation and present a number of examples of finite and infinite sequences of polynomial eigenfunctions for differential operators of order 1 and 2.
The talk is based on a joint work with Alexander Dyachenko.